Answers
ΔABD and ΔBCD are similar, therefore:
[tex]\dfrac{y}{5}=\dfrac{11}{y}\ \ \ |\cross\ multiply\\\\y^2=55\to y=\sqrt{55}[/tex]
Use Pythagorean theorem:
[tex]x^2=5^2+(\sqrt{55})^2\\\\x^2=25+55\\\\x^2=80\to x=\sqrt{80}\\\\x=\sqrt{16\cdot5}\\\\x=\sqrt{16}\cdot\sqrt5\\\\\boxed{x=4\sqrt5}[/tex]
Related Questions
Find the value of x and the value of y
Answers
Since the two 45-deg angles are congruent, their opposite sides are also congruent. That makes y = 5.
This triangle is a 45-45-90 triangle. In a 45-45-90 triangle, the legs are congruent and the hypotenuse is sqrt(2) times the length of the legs.
The hypotenuse has length x, so x = 5 * sqrt(2) = 5sqrt(2)
Answer: B. x = 5sqrt(2), y = 5
Which pairs of rectangles are similar polygons? Select Similar or Not Similar for each pair of rectangles.
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108/72 = 1.5
132/80= 1.65
I would say A and B are similar, not C
Step-by-step explanation: We are given three rectangular figures A, B and C.
We need to determine which polygons are similar and which are not.
Note: The sides of similar figures are in proportion.
Let us check first A and B figures.
150/108 = 50/36
100/72 = 50/ 36.
We can see 150/108 = 100/72 = 50/ 36.
Sides are in proportion of Polygons A and B.
So, the Polygons A and B are Similar.Let us check first A and C figures.
150/132 = 25/22
100/80 = 5/4.
We can see 150/132 ≠ 100/80.
Sides are not in proportion of Polygons A and C.
So, the Polygons A and C are Not Similar.Let us check first B and C figures.
108/132 = 9/11.
72/80 = 9/10.
We can see 108/132 ≠ 72/80.
Sides are not in proportion of Polygons B and C.
So, the Polygons B and C are Not Similar.what is £747 by 2:7 in a ratio
Answers
747 : 9 = 83
2 · 83 = 166
7 · 83 = 581
Answer: £166 and £581
−4x−7+10x=−7+6x how many solutions
Answers
Step-by-step explanation:
[tex]-4x-7+10x=-7+6x\\\\(-4x+10x)-7=-7+6x\\\\6x-7=-7+6x\qquad\text{subtract}\ 6x\ \text{from both sides}\\\\-7=-7\qquad\bold{TRUE}\\\\Answer:\ \text{Infinitely many solutions}[/tex]
Final answer:
By simplifying the given linear equation and combining like terms, we find that the single solution is x = 0. Verification confirms that this solution is valid as it satisfies the original equation.
Explanation:
The equation presented by the student is a linear equation with the variables on both sides. To solve this equation, we will combine like terms and isolate the variable x on one side of the equation.
First, let's simplify the equation by combining like terms:
-4x - 7 + 10x = -7 + 6x
Combine x terms on the left side and numerical terms on the right:
6x = 0
Finally, divide by the coefficient of x to solve for x:
x = 0
This value of x is the single solution to the equation. It's important to note that there are no other solutions in this case, as it's a simple linear equation and not a quadratic or higher-order polynomial equation.
Verification
To verify that x = 0 is indeed a solution, we can substitute it back into the original equation:
-4(0) - 7 + 10(0) = -7 + 6(0)
All terms involving x drop out, confirming that -7 = -7 is an identity, making x = 0 a valid solution.
Does a trapezoid have obtuse angles
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Witch is bigger 8 yards or 20 feet
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8 yards x 3 feet = 24 feet
24 feet is bigger than 20 feet so 8 yards is bigger
Find the range 3, -97,-15,-42
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The range of the numbers 3, -97, -15, -42 is 100.
Explanation:The range of a set of numbers is the difference between the largest and smallest numbers in the set. To find the range of the numbers 3, -97, -15, -42, we first need to find the largest and smallest numbers. The largest number is 3 and the smallest number is -97. Subtracting the smallest number from the largest number gives us a range of 100.
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A repairman leans the top of an 8 ft ladder against the top of a stone wall the base of the ladder is 5.5 ft from the wall about how tall is the wall round to the nearest tenth of a foot
Answers
The height of the wall if A repairman leans the top of an 8 ft ladder against the top of a stone wall, the base of the ladder is 5.5 ft from the wall, is 5.81 feet.
What is trigonometry?Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine, cosine, and tangents are their names and acronyms (tan).
Given:
A repairman leans the top of an 8 ft ladder against the top of a stone wall, the base of the ladder is 5.5 ft from the wall,
Calculate the height of the wall as shown below,
Assume the height of the wall is x then,
x² + base² = ladder height²
x² + 5.5² = 8²
x² = 64 - 30.25
x² = 33.75
x = √33.75
x = 5.81 ft
Thus, the height of the wall is 5.81 feet.
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A meter stick casts a shadow 2.4 m long at the same time a flagpole casts a shadow 9.7 m long. How tall is the flagpole
Answers
We an draw tow similar triangle between the length of the shadows and the height of the stick and the pole.
Since meter stick has a length of 1 meter, the height of our smaller triangle is 1 meter. Let [tex]h[/tex] be height of of the pole. Since both triangles are similiar we can establish a proportion between their corresponding sides and solve for [tex]h[/tex]:
[tex] \frac{h}{1} = \frac{9.7}{2.4} [/tex]
[tex]h=\frac{9.7}{2.4}[/tex]
[tex]h=4.04[/tex]
We can conclude that the pole is 4.04 meters tall.
Three tables are placed side by side by side. One table is 3 feet 11 inches wide, another is 6 feet 10 inches wide, and the third is 3 feet 7 inches wide. How wide are they combined?
Answers
To find the combined width of the three tables, add up their individual widths.
Explanation:To find the combined width of the three tables, we need to add up their individual widths.
The first table is 3 feet 11 inches wide, which is equivalent to 3 feet 11 inches + 0 feet 11 inches = 3 feet 22 inches.
The second table is 6 feet 10 inches wide, which is equivalent to 6 feet 10 inches + 0 feet 10 inches = 6 feet 20 inches.
The third table is 3 feet 7 inches wide, which is equivalent to 3 feet 7 inches + 0 feet 7 inches = 3 feet 14 inches.
Adding up the widths: 3 feet 22 inches + 6 feet 20 inches + 3 feet 14 inches = 12 feet 56 inches.
Therefore, the combined width of the three tables is 12 feet 56 inches.
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Without graphing estimate the x-intercepts of the graph of f(x)=7x^2+9x+1 to the nearest tenth.
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We will use the quadratic formula to find these:
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ \\=\frac{-9\pm \sqrt{9^2-4(7)(1)}}{2(7)}=\frac{-9\pm \sqrt{81-28}}{14} \\ \\=\frac{-9\pm \sqrt{53}}{14}=\frac{-9+\sqrt{53}}{14}\text{ or } \frac{-9-\sqrt{53}}{14} \\ \\=-0.1\text{ or }-1.2[/tex]
Find the area. The figure is not drawn to scale
Answers
Answer:
D) 704 in.²
Step-by-step explanation:
The area is height × width.
So, the area =32 × 22 = 704 in.²
In the figure, m and n are rays. Which statements are true? Select each correct answer.
A: m∠3=m∠1
B: m∠2=60°
C: m∠1=60°
D: m∠3=120°
Answers
B is correct because there are 180 degrees in a triangle. 180-65-55 = 60. Angle 2 is vertical to the third angle, so angle 2 equals 60.
C is incorrect because it is an exterior angle. Exterior angles are equal to the sum of the two isolated interior angles. 65 + 55 ≠ 60.
D is correct because 3 is an exterior angle. Exterior angles are equal to the sum of the two isolated interior angles. 65 + 55 = 120.
In review, A, B, and D are correct.
I hope this helps you =)
The statements that are true about the intersecting rays are
A) m∠3 = m∠1
B) m∠2 = 60°
D) m∠3 = 120°
What are the angles formed by 2 intersecting lines?Two straight lines that intersect at the same location are said to be intersecting lines. The junction point is the place where two intersecting lines meet. Four angles are created when two lines cross. The four angles added together always equal 360 degrees.
Perpendicular lines are two straight lines that intersect and form right angles. When two perpendicular lines intersect, they form four right angles.
When lines intersect, two angle relationships are formed:
Opposite angles are congruent
Adjacent angles are supplementary
Given data ,
Let the two intersecting lines be m and n
Now , the angles formed are shown in the diagram
where the measure of ∠1 = ∠3 ( Opposite angles are congruent )
Now , the measure of ∠2 = 180° - ( 65° + 55° ) ( angles in a triangle = 180° )
The measure of ∠2 = 60°
So , the measure of ∠3 = 180° - ∠2 ( Adjacent angles are supplementary = 180° )
And , the measure of ∠3 = 120°
Hence , the angles in the intersecting lines are solved
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Which of these is a trinomial?
A.2x^3 – 7y^3
B.2x – 7
C.5xy
D.x + 2y^2 – 7
Answers
Option D, which is x + 2y^2 - 7, is a trinomial as it contains exactly three terms.
Explanation:A trinomial is an algebraic expression with three terms.
These terms are usually separated by '+' or '-' signs. Let's examine the options given to identify a trinomial:
A. 2x^3 - 7y^3 has two terms and is a binomial.B. 2x - 7 has two terms and is a binomial.C. 5xy has only one term and is a monomial.D. x + 2y^2 - 7 has three terms and is a trinomial.Therefore, Option D is the correct answer as it is the expression that contains exactly three terms, making it a trinomial.
Rewrite the exponential function y = 12 (0.56)^(t/4).
Round your answer to two decimal places.
Answers
y = 12 (0.56)^(t/4)
y=12(0.56^(1/4))^t
but
0.56^(1/4)=0.8651
thus plugging the value in y we get:
y=12(0.8651)^t
in two decimal places we get:
y=12(0.87)^t
The exponential function will be written as:
y = 12 (0.56) ^ (t/4)
y=12 (0.56^ (1/4)) ^t
but
0.56^ (1/4) = 0.8651
thus plugging the value in y we get:
y=12 (0.8651) ^t
in two decimal places we get:
y=12 (0.87) ^t
find the measure of the arc or angle indicated. or find the value of x
Answers
The table represents f(x), and the graph represents g(x). Which statements about the functions are true for the interval [4, 10]?
x f(x)
______
3 1.33
4 1
5 0.8
6 0.66
10 0.4
Select ALL that apply
1- The average rate of change of f(x) is greater than the average rate of change of g(x).
2- The average rate of change of f(x) is less than the average rate of change of g(x).
3- Both functions have the same average rate of change.
4- The average rate of change of f(x) is 0.1, and the average rate of change of g(x) is 0.25.
5- The average rate of change of f(x) is -0.1, and the average rate of change of g(x) is -0.25.
Answers
Answer:
1- The average rate of change of f(x) is greater than the average rate of change of g(x).
5- The average rate of change of f(x) is -0.1, and the average rate of change of g(x) is -0.25.
Step-by-step explanation:
average rate of change of a function h(x) in the interval [a, b] is computed as follows:
average rate of change = h(b) - h(a)/(b - a)
So, for f(x) (see table):
average rate of change = f(10) - f(4)/(10 - 4) = (0.4 - 1)/(10 - 4) = -0.1
And for g(x) (see figure):
average rate of change = g(10) - g(4)/(10 - 4) = (1 - 2.5)/(10 - 4) = -0.25
A = bh/2 solve for b
Answers
Cross multiply:
[tex]2A = bh [/tex]
Divide by h on both sides:
[tex]b = \dfrac{2A}{h} [/tex]
The value of b in the equation is [tex]b=\frac{2A}{h}[/tex].
What is simplification of an equation?Simplification of an equation is the process of writing an equation in the most efficient and compact form without affecting the value of the original equation.
For the given situation,
The equation is [tex]A=\frac{bh}{2}[/tex]
The equation can be simplified as
⇒ [tex]A=\frac{bh}{2}[/tex]
⇒ [tex]2A=bh[/tex]
⇒ [tex]b=\frac{2A}{h}[/tex]
Hence we can conclude that the value of b in the equation is [tex]b=\frac{2A}{h}[/tex].
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How would you find the area of this shape? ( rectangle and congruent triangle )
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what is the solution to the equation 1/3 x = 6
Answers
Multiply by 3 on both sides:
x = 18
Answer: x = 18
the perimeter of the rectangle is 42 units. what are the dimensions?
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A cube that has side lengths measuring 7 inches
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A cube with side lengths measuring 7 inches means that each side of the cube is 7 inches long.
To find the volume of the cube, you multiply the length, width, and height of the cube since all sides are equal:
Volume = length × width × height
For a cube, all these measurements are the same, so you can simply cube the length of one side:
Volume = 7 inches × 7 inches × 7 inches
Volume = 7³ cubic inches
Volume = 343 cubic inches
So, the volume of the cube is 343 cubic inches.
A cube with side lengths measuring 7 inches implies that each side of the cube is 7 inches long.
To find the volume of the cube, we use the formula for the volume of a cube, which is side length cubed.
Since all sides of a cube are equal, we simply cube the length of one side: 7 inches × 7 inches × 7 inches. This equals 7³ = 343 cubic inches.
Therefore, the volume of the cube is 343 cubic inches. In a cube, all sides, angles, and faces are congruent, making it a regular polyhedron with 6 square faces.
Complete Question:
A cube that has side lengths measuring 7 inches.
In The Figure Below, Find X.
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I attached a picture of how i worked this out.
The highlighted lines in blue are alternate angles therefore will be the same
____________________________________________
Note: "x + 32 = 123 " ;
{since: 1) the "123° angle" shown in the diagram ; AND:
2) the angle formed by the 2 (two) angles:
" ∠x" and the "32° angles (shown in the diagram) } ;
____________________________________________________
→ are "altenrate interior angles";
and "alternate interior angles" are congruent.
____________________________________________________
So, x = 123 - 32 = 91 .
____________________________________________________
The answer is: " x = 91 " .
____________________________________________________
setsuko has a rectangular piece of farbric that is 5/6 yard wide. The area of the fabric is 5/16 square yard. How long is setsuko's fabric
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ehat is the value of y=3x2-18x+15
Answers
The value of the equation y = 3x^2 - 18x + 15 can be found by substituting different values of x and calculating the corresponding value of y.
Explanation:The value of the equation y = 3x^2 - 18x + 15 can be found by substituting different values of x and calculating the corresponding value of y. For example, if we substitute x = 1, we get y = 3(1)^2 - 18(1) + 15 = 0. So, when x = 1, y is 0.
To find more values, we can create a table of values by substituting different x values into the equation. The resulting values of y can be plotted on a graph to see the pattern and shape of the equation.
Table of Values:
x = 0, y = 15x = 1, y = 0x = 2, y = 9x = 3, y = 18This equation represents a quadratic function in the form of y = ax^2 + bx + c, where a = 3, b = -18, and c = 15.
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Given that the measurement is in centimeters, find the area of the circle to the nearest tenth.(Use 3.14 for n) Radius is 3
A) 18.9 cm2
B) 28.3 cm2
C) 37.7 cm2
D) 88.7 cm2
Answers
The answer is a)18.9 cm2
How I got my answer:
circumference=2*π *r
circumference=2*3.14*3
=18.84cm2=rounded to the nearest tenth=18.8cm2
The closest answer is 18.9cm2
Hope this helps you.
Answer:
The area of the circle is equal 28.3 cm² to the nearest tenth.
Step-by-step explanation:
To find the area of the circle that has a radius of 3, we will simply use the formula;
Area of a cirle = π r²
where π is a constand and r is the radius.
From the question given π = 3.14 and r=3
We can now proceed to insert the value into the formula;
Area of a cirle = π r²
=3.14×3²
=3.14×9
=28.26
≈28.3 cm²
Therefore, the area of the circle is equal 28.3 cm² to the nearest tenth.
If the probability of winning a carnival game was 2/5 and Max played it five times, write an expression that would calculate the probability he won the first three games and lost the last two
Answers
Prob(losing carnival game) = 3/5
Prob (Max wins first 3 games, but loses last 2 games)
= Prob(Max wins game 1) * Prob(Max wins game 2) * Prob(Max wins game 3) * Prob(Max loses game 4) * Prob(Max loses game 5)
The probability of Max winning the first three games while losing the rest two is 0.023.
What is Probability?The probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
As it is given that the probability of winning the game is 2/5. Since the sum of all the probability of an event is 1, therefore, the probability of losing the game can be written as,
Sum of all probability = Probability of winning + Probability of losing
[tex]1 = \dfrac25+\text{(Probability of losing)}\\\\\text{(Probability of losing)}=\dfrac35[/tex]
Thus, the probability of losing the game is 3/5.
As we need to calculate the probability of Max winning the first three games while he losing the rest two. Therefore,
[tex]P = \dfrac25 \times \dfrac25 \times \dfrac25 \times \dfrac35 \times \dfrac35 = \dfrac{72}{3125} = 0.023[/tex]
Hence, the probability of Max winning the first three games while losing the rest two is 0.023.
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Car A gets 25 miles per gallon and costs $13,000. Car B is a hybrid that gets 45 miles per gallon, but costs $25,000. Assume you drive 15,000 miles per year and that gas will cost $4 per gallon for the foreseeable future. How many years will it take for Car B's better fuel economy to outweigh its higher initial cost?
Answers
The cost of fuel consumed in n years by car B is
[tex]=n\times \frac{15000\:miles}{year}\times \frac{1\:gallon}{45\:miles}\times \frac{4\:dollars}{gallon}[/tex]
Equate the initial cost to the cost of fuel
[tex]25000=n\times \frac{15000\:miles}{year}\times \frac{1\:gallon}{45\:miles}\times \frac{4\:dollars}{gallon}[/tex]
[tex]25000=\frac{4000n}{3}[/tex]
[tex]n=\frac{25000\left(3\right)}{4000}[/tex]
[tex]n=18.75[/tex]
It will take 18.75 years for Car B's better fuel economy to outweigh its higher initial cost.
Answer: The answer is B) 11.25
Step-by-step explanation: I got it right
A cereal box is a rectangular prism that is 8 inches long and 2 1/2 inches wide. The volume of the box is 200 in^3. What is the height of the box
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Part A: Write an algebraic expression for 6 more than 7 times a number.
Part B: Write a verbal expression for 3(n + 8).
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B) The product of 3 and the sum of a number and 8.